It looks like a third party Twitter app has beaten the official Twitter app in the race to offer push notifications. The third party app is called MahTweets and they have announced that push notifications will soon be possible. The support will include mentions and direct messages however the catch is that the app is not yet available in the Markeplace. That said, it has been submitted and it waiting approval, sadly though, it has already been submitted and rejected two times in the past. Otherwise, the MahTweets app seems like a worthy competitor with other features including read only support for Yammer and Tumblr as well as TwitPic uploads, Geotagging, themes and support for multiple accounts. The one drawback comes in with lists, which are not yet supported. But with that, the MahTweets account is available for free so given that, it seems worthy of a download just to see if it measures up for your needs.